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2017 | Nr 59 | 57--74
Tytuł artykułu

Hermite-Hadamard type inequalities with applications

Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article first, we give an integral identity and prove some Hermite-Hadamard type inequalities for the function ƒ such that |ƒ''|q is convex or concave for q ≥ 1. Second, by using these results, we present applications to ƒ-divergence measures. At the end, we obtain some bounds for special means of real numbers and new error estimates for the trapezoidal formula.
Wydawca

Rocznik
Tom
Strony
57--74
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
autor
  • Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan, adilswati@gmail.com
autor
  • Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan, atahir623@gmail.com
autor
Bibliografia
  • [1] Abramovich S., Barić J., Pečarić J., Fejer and Hermite-Hadamard type inequalities for superquadratic functions, J. Math. Anal. Appl., 344(2008), 1048-1056.
  • [2] Abramovich S., Farid G., Pečarić J., More about Hermite-Hadamard inequalities, Cauchy’s mean and superquadracity, J. Inequal. Appl. 2010, Article ID 102467 (2010).
  • [3] Agarwal R.P., Dragomir S.S., An application of Hayashi’s inequality for differentiable functions, Comput. Math. Appl., 32(6)(1996), 95-99.
  • [4] Ali S.M., Silvey S.D., A general class of coefficients of divergence of one distribution from another, J. Roy. Statist. Soc. Sec B, 28(1966), 131-142.
  • [5] Alomeri M., Darus M., Dragomir S.S., New inequalities of HermiteHadamard type for functions whose second derivatives absolute values are quasi-convex, Tamkang J. Math., 41(4)(2010), 353-359.
  • [6] Burbea I., Rao C.R., On the convexity of some divergence measures based on entropy function, IEEE Trans. Inf. Th., 28(3)(1982), 489-495.
  • [7] Csisźar I., Information-type measures of difference of probability distributions and indirect observations, Studia Math. Hungarica, 2(1967), 299-318.
  • [8] Dragomir S.S., Pečarić J., Sándor J., A note on the Jensen-Hadamard’s inequality, Anal. Num. Ther. Approx., 19(1990), 29-34.
  • [9] Dragomir S.S., Two mappings in connection to Hadamard’s inequality, J. Math. Anal. Appl., 167(1992), 49-56.
  • [10] Dragomir S.S., On Hadamard’s inequalities for convex functions, Mat. Balkanica, 6(1992), 215-222.
  • [11] Dragomir S.S., Buse C., Refinements of Hadamard’s inequality for multiple integrals, Utilitas Math., 47(1995), 193-198.
  • [12] Dragomir S.S., Pečarić J., Persson, L.E., Some inequalities of Hadamard type, Soochow J. Math., 21(1995), 335-341.
  • [13] Dragomir S.S., Wang S., An inequality of Ostrowski-Griiss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rule, Comput. Math. Appl., 3(11)(1997), 15-20.
  • [14] Dragomir S.S., Agarwal R.P., Two inequalities for differentiable mappings and applications to special means of real numbers and trapezoidal formula, Appl. Math. Lett., 5(1998), 91-95.
  • [15] Dragomir S.S., Pearce C.E.M., Selected topics on Hermite-Hadamard inequalities and applications, RGMIA Monographs, Victoria University (2000).
  • [16] Hadamard J., Étude sur les propriétés des fonctions entières et en particulier dune fonction considérée par Riemann, J. Math. Pures Appl., 58(1893), 171-215.
  • [17] Havrda J.H., Charvat F., Quantification method classification process concept of structural-entropy, Kybernetika, 3(1967), 30-35.
  • [18] Kapur J.N., A comparative assessment of various measures of directed divergence, Advances in Management Studies, 3(1984), 1-16.
  • [19] Kirmaci U.S., Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput., 147(2004), 137-146.
  • [20] Kirmaci U.S., Ozdemir M.E., On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput., 153(2004), 361-368.
  • [21] Kirmaci U.S., Bakula M.K., Ozdemir M.E., Pečarić J., Hadamard type inequalities for s-convex functions, Appl. Math. Comput., 193(1)(2007), 26-35.
  • [22] Kirmaci U.S., Improvement and further generalization of inequalities for differentiable mappings and applications, Comput. Math. Appl., 55(2008), 485-493.
  • [23] Kullback S., Leibler R.A., On information and sufficiency, Ann. Math. Stat., 22(1951), 79-86.
  • [24] Lin J., Divergence measures based on the Shannon entropy, IEEE Trans. Inf. Th., 37(1)(1991), 145-151.
  • [25] Ozdemir M.E., A theorem on mappings with bounded derivatives with applications to quadrature rules and means, Appl. Math. Comput., 138(2003), 425-434.
  • [26] Ozdemir M.E., Kirmaci U.S., Two new theorems on mappings uniformly continuous and convex with applications to quadrature rules and means, Appl. Math. Comput., 143(2003), 269-274.
  • [27] Pearce C.E.M., Pečarić J., Inequalities for differentiable mapping with application to special means and quadrature formula, Appl. Math. Lett., 13(2000), 51-55.
  • [28] Pečarić J., Prochan F., Tong Y.L., Convex Functions, Partial Ordering and Statistical Applications, Academic Press, New York, (1991).
  • [29] Renyi A., On measures of entropy and information, Proc. Fourth Berkeley Symp. Math. Stat. and Prob., University of California Press, 1(1961), 547-561.
  • [30] Set E., Iscan I., Sarikaya M.Z., Ozdemir M.E., On new inequalities of Hermite-Hadamard-Fejer type for convex functions via fractional integrals, Appl. Math. Comput., 259(2015), 875-881.
  • [31] Shioya H., Da-Te T., A generalization of Lin divergence and the derivative of a new information divergence, Elec. and Comm. in Japan, 78(7)(1995), 37-40.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.baztech-099da420-60d6-4184-bd58-e6934f2b1e0b
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